Abstract

In the international standard (International Organization for Standardization 11551) for measuring the absorptance of optical components (i.e., laser calorimetry), the absorptance is obtained by fitting the temporal behavior of laser irradiation-induced temperature rise to a homogeneous temperature model in which the infinite thermal conductivity of the sample is assumed. In this paper, an accurate temperature model, in which both the finite thermal conductivity and size of the sample are taken into account, is developed to fit the experimental temperature data for a more precise determination of the absorptance. The difference and repeatability of the results fitted with the two theoretical models for the same experimental data are compared. The optimum detection position when the homogeneous model is employed in the data-fitting procedure is also analyzed with the accurate temperature model. The results show that the optimum detection location optimized for a wide thermal conductivity range of 0.250W/m·K moves toward the center of the sample as the sample thickness increases and deviates from the center as the radius and irradiation time increase. However, if the detection position is optimized for an individual sample with known sample size and thermal conductivity by applying the accurate temperature model, the influence of the finite thermal conductivity and sample size on the absorptance determination can be fully compensated for by fitting the temperature data recorded at the optimum detection position to the homogeneous temperature model.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  19. M. Q. Liu and B. C. Li, “Analysis of temperature and deformation fields in an optical coating sample,” Acta Phys. Sin. 57, 3402–3409 (2008).
  20. M. J. Weber, Handbook of Optical Materials (CRC, 2003).
  21. http://www.corning.com/specialty materials/products_capabilities/HPFS.aspx.

2008

M. Q. Liu and B. C. Li, “Analysis of temperature and deformation fields in an optical coating sample,” Acta Phys. Sin. 57, 3402–3409 (2008).

2007

2005

2003

H. Blaschke, M. Jupé, and D. Ristau, “Absorptance measurements for the DUV spectral range by laser calorimetry,” Proc. SPIE 4932, 467–474 (2003).
[CrossRef]

2000

1999

1998

1996

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption at 532nm and 1064nm according to ISO/FDIS 11551,” Proc. SPIE 2870, 483–494 (1996).
[CrossRef]

E. Eva and K. Mann, “Calorimetric measurement of two-photon absorption and color-center formation in ultraviolet-window materials,” Appl. Phys. A. 62, 143–149(1996).
[CrossRef]

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption and transmissivity with sub-ppm sensitivity,” Proc. SPIE 2775, 148–158 (1996).
[CrossRef]

1995

H. Grönbeck and M. Reichling, “Harmonic heat flow in anisotropic thin films,” J. Appl. Phys. 78, 6408–6413 (1995).
[CrossRef]

1994

M. Reichling and H. Grönbeck, “Harmonic heat flow in isotropic layered systems and its use for thin film thermal conductivity measurements,” J. Appl. Phys. 75, 1914–1922 (1994).
[CrossRef]

1990

1986

1980

1979

H. B. Rosenstock, “Absorption measurements by laser calorimetry,” J. Appl. Phys. 50, 102–110 (1979).
[CrossRef]

1975

1971

M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046(1971).
[CrossRef]

Amer, N. M.

Bernal G., E.

Blaschke, H.

H. Blaschke, M. Jupé, and D. Ristau, “Absorptance measurements for the DUV spectral range by laser calorimetry,” Proc. SPIE 4932, 467–474 (2003).
[CrossRef]

Boccara, A. C.

Bublitz, S.

Chow, R.

Commandre, M.

Ebert, J.

Eva, E.

E. Eva and K. Mann, “Calorimetric measurement of two-photon absorption and color-center formation in ultraviolet-window materials,” Appl. Phys. A. 62, 143–149(1996).
[CrossRef]

Fournier, D.

Gallais, L.

Grönbeck, H.

H. Grönbeck and M. Reichling, “Harmonic heat flow in anisotropic thin films,” J. Appl. Phys. 78, 6408–6413 (1995).
[CrossRef]

M. Reichling and H. Grönbeck, “Harmonic heat flow in isotropic layered systems and its use for thin film thermal conductivity measurements,” J. Appl. Phys. 75, 1914–1922 (1994).
[CrossRef]

Gross, T.

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption at 532nm and 1064nm according to ISO/FDIS 11551,” Proc. SPIE 2870, 483–494 (1996).
[CrossRef]

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption and transmissivity with sub-ppm sensitivity,” Proc. SPIE 2775, 148–158 (1996).
[CrossRef]

Jackson, W.

Jupé, M.

H. Blaschke, M. Jupé, and D. Ristau, “Absorptance measurements for the DUV spectral range by laser calorimetry,” Proc. SPIE 4932, 467–474 (2003).
[CrossRef]

Kufert, S.

Kuo, P. K.

Li, B. C.

M. Q. Liu and B. C. Li, “Analysis of temperature and deformation fields in an optical coating sample,” Acta Phys. Sin. 57, 3402–3409 (2008).

B. C. Li, S. Martin, and E. Welsch, “Pulsed top-hat beam thermal lens measurement for ultraviolet dielectric coatings,” Opt. Lett. 24, 1398–1400 (1999).
[CrossRef]

Liu, M. Q.

M. Q. Liu and B. C. Li, “Analysis of temperature and deformation fields in an optical coating sample,” Acta Phys. Sin. 57, 3402–3409 (2008).

Mann, K.

E. Eva and K. Mann, “Calorimetric measurement of two-photon absorption and color-center formation in ultraviolet-window materials,” Appl. Phys. A. 62, 143–149(1996).
[CrossRef]

Martin, S.

Mühlig, C.

Munidasa, M.

Reichling, M.

H. Grönbeck and M. Reichling, “Harmonic heat flow in anisotropic thin films,” J. Appl. Phys. 78, 6408–6413 (1995).
[CrossRef]

M. Reichling and H. Grönbeck, “Harmonic heat flow in isotropic layered systems and its use for thin film thermal conductivity measurements,” J. Appl. Phys. 75, 1914–1922 (1994).
[CrossRef]

Ristau, D.

H. Blaschke, M. Jupé, and D. Ristau, “Absorptance measurements for the DUV spectral range by laser calorimetry,” Proc. SPIE 4932, 467–474 (2003).
[CrossRef]

U. Willamowski, D. Ristau, and E. Welsch, “Measuring the absolute absorptance of optical laser components,” Appl. Opt. 37, 8362–8370 (1998).
[CrossRef]

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption and transmissivity with sub-ppm sensitivity,” Proc. SPIE 2775, 148–158 (1996).
[CrossRef]

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption at 532nm and 1064nm according to ISO/FDIS 11551,” Proc. SPIE 2870, 483–494 (1996).
[CrossRef]

D. Ristau and J. Ebert, “Development of a thermographic laser calorimeter,” Appl. Opt. 25, 4571–4578 (1986).
[CrossRef] [PubMed]

Rosenstock, H. B.

H. B. Rosenstock, “Absorption measurements by laser calorimetry,” J. Appl. Phys. 50, 102–110 (1979).
[CrossRef]

Sparks, M.

M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046(1971).
[CrossRef]

Taylor, J. R.

Triebel, W.

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC, 2003).

Welling, H.

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption at 532nm and 1064nm according to ISO/FDIS 11551,” Proc. SPIE 2870, 483–494 (1996).
[CrossRef]

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption and transmissivity with sub-ppm sensitivity,” Proc. SPIE 2775, 148–158 (1996).
[CrossRef]

Welsch, E.

Willamowski, U.

U. Willamowski, D. Ristau, and E. Welsch, “Measuring the absolute absorptance of optical laser components,” Appl. Opt. 37, 8362–8370 (1998).
[CrossRef]

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption and transmissivity with sub-ppm sensitivity,” Proc. SPIE 2775, 148–158 (1996).
[CrossRef]

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption at 532nm and 1064nm according to ISO/FDIS 11551,” Proc. SPIE 2870, 483–494 (1996).
[CrossRef]

Wu, Z. L.

Acta Phys. Sin.

M. Q. Liu and B. C. Li, “Analysis of temperature and deformation fields in an optical coating sample,” Acta Phys. Sin. 57, 3402–3409 (2008).

Appl. Opt.

Appl. Phys. A.

E. Eva and K. Mann, “Calorimetric measurement of two-photon absorption and color-center formation in ultraviolet-window materials,” Appl. Phys. A. 62, 143–149(1996).
[CrossRef]

J. Appl. Phys.

M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046(1971).
[CrossRef]

H. B. Rosenstock, “Absorption measurements by laser calorimetry,” J. Appl. Phys. 50, 102–110 (1979).
[CrossRef]

M. Reichling and H. Grönbeck, “Harmonic heat flow in isotropic layered systems and its use for thin film thermal conductivity measurements,” J. Appl. Phys. 75, 1914–1922 (1994).
[CrossRef]

H. Grönbeck and M. Reichling, “Harmonic heat flow in anisotropic thin films,” J. Appl. Phys. 78, 6408–6413 (1995).
[CrossRef]

Opt. Lett.

Proc. SPIE

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption at 532nm and 1064nm according to ISO/FDIS 11551,” Proc. SPIE 2870, 483–494 (1996).
[CrossRef]

H. Blaschke, M. Jupé, and D. Ristau, “Absorptance measurements for the DUV spectral range by laser calorimetry,” Proc. SPIE 4932, 467–474 (2003).
[CrossRef]

U. Willamowski, T. Gross, D. Ristau, and H. Welling, “Calorimetric measurement of optical absorption and transmissivity with sub-ppm sensitivity,” Proc. SPIE 2775, 148–158 (1996).
[CrossRef]

Other

International Organization for Standardization, “Test method for absorptance of optical laser components,” ISO 11551:2003(E) (International Organization for Standardization, 2003).

M. J. Weber, Handbook of Optical Materials (CRC, 2003).

http://www.corning.com/specialty materials/products_capabilities/HPFS.aspx.

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Figures (7)

Fig. 1
Fig. 1

Temperature data simulated with the accurate model and the corresponding best fits to the homogeneous model for different irradiation periods: (a) 30 s , (b) 120 s .

Fig. 2
Fig. 2

Experimental temperature data and corresponding best fits to the accurate and homogeneous models, respectively, for (a) 30 s and (b) 120 s irradiation periods.

Fig. 3
Fig. 3

Comparison of the fitted absorptance values with the accurate and homogeneous models for different irradiation periods for a HR mirror on fused silica substrate.

Fig. 4
Fig. 4

Absorptance values obtained by fitting the temperature data simulated with the accurate model to the homogeneous model versus the thermal conductivity for different detection positions.

Fig. 5
Fig. 5

Simulated temperature data at the optimum detection position and corresponding best fits for thermal conductivity (a) 0.2 W / m · K and (b) 10 W / m · K , respectively.

Fig. 6
Fig. 6

Optimum detection position versus (a) the size and (b) the radius of the sample, respectively.

Fig. 7
Fig. 7

Optimum detection position and corresponding fitted absorptance value versus the irradiation period. For comparison, the fitted absorptance value obtained at the 7 mm position for a BK7 sample is also presented.

Tables (1)

Tables Icon

Table 1 Optimum Detection Position, Corresponding Fitted Absorptance Value, and mean Square Variance for Irradiation Time 30 to 180 s for a Coated BK7 Sample with Assumed Thermal Conductivity of 1.1 W / m · K

Equations (14)

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2 T ( r , z , t ) 1 D T ( r , z , t ) t = Q ( r , z , t ) K th .
T ( r , z , t ) z | z = 0 + H T ( r , z , t ) = 0 , T ( r , z , t ) z | z = d + H T ( r , z , t ) = 0 , T ( r , z , t ) r | r = b + H T ( r , z , t ) = 0 ,
T ( r , z , t ) t = 0 = 0.
Q ( r , z , t ) = { 2 ( 1 R f ) P π a 2 α exp ( 2 r 2 / a 2 ) exp ( α z ) ( 0 < t t 0 ) 0 ( t > t 0 ) ,
T ( r , z , t ) = D K th m = 1 p = 1 1 N ( β m ) · N ( η p ) · J 0 ( β m r ) · ( η p cos ( η p z ) + H sin ( η p z ) ) · ( 1 exp ( D ( β m 2 + η p 2 ) t ) ) · 1 D ( β m 2 + η p 2 ) · 2 · P · ( 1 R f ) π a 2 · a 2 4 exp ( β m 2 a 2 8 ) · { α η p α 2 + η p 2 { exp ( α d ) · [ α cos ( η p d ) + η p sin ( η p d ) ] + α } + α H α 2 + η p 2 { exp ( α d ) · [ α sin ( η p d ) η p cos ( η p d ) ] + η p } } ( 0 < t t 0 ) ,
T ( r , z , t ) = D K th m = 1 p = 1 1 N ( β m ) · N ( η p ) · J 0 ( β m r ) · ( η p cos ( η p z ) + H sin ( η p z ) ) · ( 1 exp ( D ( β m 2 + η p 2 ) t 0 ) ) · exp ( D ( β m 2 + η p 2 ) ( t t 0 ) ) · 1 D ( β m 2 + η p 2 ) · 2 · P · ( 1 R f ) π a 2 · a 2 4 exp ( β m 2 a 2 8 ) · { α η p α 2 + η p 2 { exp ( α d ) · [ α cos ( η p d ) + η p sin ( η p d ) ] + α } + α H α 2 + η p 2 { exp ( α d ) · [ α sin ( η p d ) η p cos ( η p d ) ] + η p } } ( t > t 0 ) .
T ( r , z , t ) = D K th A 0 P π a 2 m = 1 p = 1 1 N ( β m ) · N ( η p ) · J 0 ( β m r ) · ( η p cos ( η p z ) + H sin ( η p z ) ) · ( 1 exp ( D ( β m 2 + η p 2 ) t ) ) · η p D ( β m 2 + η p 2 ) · a 2 2 · exp ( β m 2 a 2 8 ) ( 0 < t t 0 ) ,
T ( r , z , t ) = D K th A 0 P π a 2 m = 1 p = 1 1 N ( β m ) · N ( η p ) · J 0 ( β m r ) · ( η p cos ( η p z ) + H sin ( η p z ) ) · η p D ( β m 2 + η p 2 ) · a 2 2 · exp ( β m 2 a 2 8 ) · ( 1 exp ( D ( β m 2 + η p 2 ) t 0 ) ) · ( exp ( D ( β m 2 + η p 2 ) ( t t 0 ) ) ( t > t 0 ) ,
H J o ( β m b ) = β m J 1 ( β m b ) 1 N ( β m ) = 2 J 0 2 ( β m b ) · β m 2 b 2 ( H 2 + β m 2 ) ,
tan ( η p d ) = 2 η p · H η p 2 H 2 1 N ( η p ) = 2 ( d + H η p 2 + H 2 ) ( η p 2 + H 2 ) + H .
d T ( t ) d t = A 0 P m c γ T ( t ) , γ = 2 h ρ c ( 1 b + 1 d )
T = { 0 t t d A 0 · P γ · m c · ( 1 exp ( γ ( t t d ) ) ) t d < t t 0 A 0 · P γ · m c · ( 1 exp ( γ ( t 0 t d ) ) ) · exp ( γ ( t t 0 ) ) t > t 0 .
T = { 0 t d 1 t A 0 · P γ · m c · ( 1 exp ( γ ( t t d 1 ) ) ) t d 1 < t t d 2 A 0 · P γ · m c · ( 1 exp ( γ ( t 0 t d 1 ) ) ) · exp ( γ ( t t d 2 ) ) t > t d 2 .
var = i = 1 n ( T theo ( t i ) T exp ( t i ) ) 2 i = 1 n ( T exp ( t i ) ) 2 ,

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